Snapping points of a roughly spherical mesh exactly onto a sphere
To sphere:

You could try AltShiftS>To Sphere:

From the wiki:


  The To Sphere transformation will give the selection spherical qualities.


Example:



Shrinkwrap:

Or using the Shrinkwrap modifier to shrink your mesh to a sphere object.

From the wiki:


  The Shrinkwrap modifier allows an object to “shrink” to the surface of another object. It moves each vertex of the object being modified to the closest position on the surface of the given mesh (using one of the three methods available).


You could add a shrinkwrap modifier to your mesh and set the Target to a sphere: